Euler's Theorems: Circuit, Path & Sum of Degrees


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question 1 of 3

If a graph has 15 edges, what must the degrees of the vertices add up to?

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1. The total number of degrees in a graph is 20. How many edges does it have?

2. What can be said about this graph?

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About This Quiz & Worksheet

The quiz will give you limited details about a graph, such as the number of edges or vertices. You will need to use that information to infer other characteristics of the graph. Some other questions will present you with the image of a graph and require you to answer questions about its various properties.

Quiz & Worksheet Goals

In order to answer these questions correctly, you will need to understand the following definitions:

  • Edges and vertices
  • Degrees in a graph
  • Euler circuits
  • Euler paths

Skills Practiced

The quiz will help you practice these skills:

  • Making connections - use understanding of the concept of circuits and graphs
  • Problem solving - use acquired knowledge to solve circuit practice problems
  • Defining key concepts - ensure that you can accurately define main phrases, such as edges and vertices
  • Distinguishing differences - compare and contrast topics from the lesson, such as Euler paths and Euler circuits

Additional Learning

After you complete the quiz, peruse the related lesson entitled Euler's Theorems: Circuit, Path & Sum of Degrees. The lesson covers these topics:

  • Reviewing Euler's circuit theorem
  • Analyzing Euler's path theorem
  • Surveying Euler's sum of degrees theorem
  • Utilizing the theorems to investigate graphs